Nine years ago, the company bought two camshaft factories that employed about 500 people in Michigan. By 2007 both were shut down. Now Asimco manufactures the same components in China on government-donated land in a coastal region that China has designated an export base, where companies are eligible for the sort of subsidies Mr. Romney says create an unfair trade imbalance.

But there is a twist to the Asimco story that would not fit neatly into a Romney stump speech: Since 2010, it has been owned by Bain Capital, the private equity firm founded by Mr. Romney, who has as much as $2.25 million invested in three Bain funds with large stakes in Asimco and at least seven other Chinese businesses, according to his 2012 candidate financial disclosure and other documents.

That and other China-related holdings by Bain funds in which Mr. Romney has invested are a reminder of how he inhabits two worlds that at times have come into conflict during his campaign for the White House.

As a candidate, Mr. Romney uses China as a punching bag. He accuses Beijing of unfairly subsidizing Chinese exports, artificially holding down the value of its currency to keep exports cheap, stealing American technology and hacking into corporate and government computers.

“How is it China’s been so successful in taking away our jobs?” he asked recently. “Well, let me tell you how: by cheating.”

But his private equity dealings, both while he headed Bain and since, complicate that message.

Mr. Romney’s campaign insists he has no control over his investments since they are held in a blind trust. That said, a confidential prospectus for one of the Bain funds, obtained by The New York Times, promotes China as a good investment for some of the same reasons that Mr. Romney has said concern him: “Strong fundamentals” like manufacturing wages 85 percent lower than what Americans earn, vast foreign exchange reserves and the likelihood that China will surpass the United States as the world’s largest economy.

“Accordingly, Bain Capital expects to see an increasing array of high-growth companies available for investment,” the prospectus says, noting the relative dearth of private equity in China.

Among the companies in which the Bain funds have invested is a global auto parts maker that is in the process of closing a factory in Illinois and moving most of the equipment and jobs to Jiangsu Province, where the Chinese government has built it a new plant; a Chinese electronics retailer accused by Microsoft of selling computers with pirated software; and a Hong Kong-based Chinese appliance maker that was sued for copying another company’s design for a deep-fat fryer.

Asked if Mr. Romney sees any conflict between his Bain investments in China and his policy positions, the campaign said: “Only the president has the power to level the playing field with China. No private citizen can do that alone.”

Blind Trust

The campaign said Mr. Romney put his fortune, estimated at $250 million, in a “blind trust” when he became Massachusetts governor in 2003. “The trustee of the blind trust has said publicly that he will endeavor to make the investments in the blind trust conform to Governor Romney’s positions, and whenever it comes to his attention that there is something inconsistent, he ends the investment,” the statement said.

Should Mr. Romney become president, however, the structure of the trust would most likely not meet the federal requirements for independent management. It is managed by a Boston-based law firm, Ropes & Gray, that has a long history of doing legal work for both Mr. Romney and Bain Capital, including representing some of the same Bain funds in which it invested Mr. Romney’s money.

Bain Capital declined to comment on specific investments, but said in a statement that its Chinese holdings “are consistent with the widely accepted principle that the private sector has a critical role to play in the continuing interdependence of the world’s economies.”

For many sophisticated and wealthy investors, as well as for ordinary workers invested in pension funds, China is a part of any diversified investment strategy. President Obama, a former Illinois state senator, has as much as $100,000 in a state retirement plan that contains shares of Sensata Technologies, the same auto parts company controlled by Bain that is closing its Illinois factory.

Last year, Mr. Romney’s trust sold its stake in an array of foreign holdings, including two Chinese state-owned companies: an oil company and a bank that have done business in Iran. But Mr. Romney continues to have money in Bain funds with sizable holdings in China.

He has as much as $250,000 in the Bain Capital Asia Fund and as much as $1 million each in Bain Capital Funds IX and X, all Cayman Islands entities used by Bain to make sizable investments in China, according to the 2012 candidate financial disclosures and confidential Bain prospectuses obtained by The Times through a public records request.

Among those funds’ holdings is $234 million that Bain invested in 2009 in Gome Electrical Appliances, a major Chinese retailer that was accused byMicrosoft this year of selling computers with pirated software. In 2007, Bain’s Asia fund also invested $39 million in Feixiang Group, a Chinese producer and exporter of chemicals that is a designated “state high-tech enterprise,” making it eligible for tax breaks and other government incentives. Ropes & Gray represented Bain in the partial sale of Feixiang three years later for a 53 percent return on the fund’s investment.

The Asia fund withdrew from another deal in 2008 that could have proved politically embarrassing to Mr. Romney. After the Bush administration objected, Bain dropped plans to team up with a Chinese technology giant, Huawei, to buy 3Com, a network equipment maker that supplies software and equipment to the Pentagon and other federal agencies.

The administration said intelligence reports indicated that Huawei, which was founded by a former People’s Liberation Army officer, posed “national security problems,” according to a lawsuit stemming from the deal’s collapse. A House Intelligence Committee report released Monday said Huawei continued to have troubling connections to the Chinese government, something the company denies.

Bain's interest in China dates to Romney era

Bain’s interest in China dates to when Mr. Romney ran the firm. During a panel discussion at the Federal Reserve Bank in Boston in February 1998, he told of touring an appliance factory in China where 5,000 employees “were working, working, working, as hard as they could, at rates of roughly 50 cents an hour.”

Not long afterward, a Bain affiliate, Brookside Capital Partners, acquired about 6 percent of Global-Tech Appliances, whose factory in many ways matched Mr. Romney’s description. The next year, Brookside and another Bain-related entity increased their stake to 9 percent, before selling their shares in 2000.

Just before Bain bought shares, a French firm accused Global-Tech of stealing its deep-fat fryer design. In a decision affirmed by the Supreme Court in 2011, the company was found to have willfully violated the French firm’s United States patent, selling the knockoffs even after it was sued.

Mr. Romney also has millions invested in a series of Bain funds that have a controlling stake in Sensata Technologies, a manufacturer of sensors and controls for vehicles, aircraft and electric motors that employs 4,000 workers in China. Since Bain took over the operation in 2006, its investment has quadrupled in value. Bain continues to own $2.6 billion worth of Sensata’s shares.

Two years ago, Sensata bought an operation that made automobile sensors in Freeport, Ill. At the first meeting with the plant’s 170 workers, Sensata managers announced that by the end of 2012 all the equipment and jobs would be relocated, mostly to Jiangsu Province. Workers have staged demonstrations, pleading for Mr. Romney to intervene on their behalf.

Chinese engineers, flown to Freeport for training on the equipment, described their salaries as a pittance compared with Freeport wages. Tom Gaulrapp, who has operated machines at the factory for 33 years, said he fears he will go bankrupt after he loses his job on Nov. 5.

“This goes to show the unbelievable hypocrisy of this man,” he said of Mr. Romney. “He talks about how we need to get tough on China and stop China from taking our jobs, and then he is making money off shipping our jobs there.”

It is often difficult to determine precisely how much Mr. Romney benefits from specific investments by Bain funds, since his money goes into a pool used to buy stakes in companies. In the case of Sensata, however, it is clearer because he reported a charitable donation of $405,000 in Sensata stock that he received as “partnership distributions” in 2010 and 2011, according to his tax returns.

Jiangsu Province, where most of the Freeport jobs are moving, is one of China’s designated “export bases” for auto parts. Asimco, the other auto parts manufacturer in Bain’s portfolio, also has factories in Jiangsu Province and three other regions designated as export bases.

The Chinese government incentives offered to companies in those “bases” set off acomplaint from the United States to the World Trade Organization last month. The United States asserted that in 2011, China spent $1 billion on grants, tax preferences, lowered interest rates and other subsidies to increase exports of auto parts in violation of fair trade rules.

Mr. Romney has been critical of these types of Chinese incentives to bolster exports.

The state-controlled Chinese Academy of Sciences has provided free research and development to Asimco, which exports at least 15 percent of its products, primarily to the United States. The authorities also gave the company land to build the factory that replaced the plants in Grand Haven, Mich.

Asimco’s China operations became a point of contention in bankruptcy proceedings that accompanied the closing of the Michigan plants. The bankruptcy trustee said that internal Asimco e-mails showed the company had transferred money to China to qualify for a Chinese tax rebate available only to manufacturers of exported products.

Jack Perkowski, the former longtime chairman of Asimco who now advises Western companies seeking to enter the Chinese market, said Asimco never benefited from export-related subsidies because most of its customers are in China. “I honestly can’t think of anything we could have gotten that was tied to the fact we were exporting,” he said.

But the company is striving for more overseas buyers. Last year Zhang Dejiang, the Chinese vice prime minister in charge of transportation, visited an Asimco assembly line and offered encouragement to workers. According to a statement on the company’s Web site, Mr. Zhang was particularly impressed that “the company’s products can rival their Western counterparts.”

Keith Bradsher contributed reporting from Beijing. Amy Qin and Shi Da contributed research from Beijing. Jeffrey E. Singer contributed research from New York.